Asynchronous Differential Evolution

In this paper we present an empirical , comparative performance, analysis of fourteen variants of Differential Evolution (DE) and Multiple Trial Vectors Differential Evolution algorithms to solve unconstrained global optimization problems. The aim is (1) to compare Multiple Trial Vectors DE, which allows each parent vector in the population to generate more than one trial vector, against the classical DE and (2) to identify the competitive variants which perform reasonably well on problems with different features. The DE and Multiple Trial Vectors DE variants are benchmarked on 6 test functions grouped by features --- unimodal separable, unimodal nonseparable, multimodal separable and multimodal non-separable. The analysis identifies the competitive variants and shows that Multiple Trial Vectors DE compares well with the classical DE.

Differential evolution is a simple yet efficient heuristic originally designed for global optimization over continuous spaces that has been used in many research areas. The question how to improve its performance is still popular and during the years, many successful methods dealing with optimal setting or hybridization of the control parameters were proposed. In this paper, we propose a novel approach based on modeling of the differential evolution dynamics by complex networks. In each generation, the individuals are mapped to the nodes and the relationships between them are modeled by the edges of the graph. Thanks to this simple visualization, the interconnection between the differential evolution convergence speed and the weighted clustering coefficients has been revealed. As a consequence, we have focused on the parents selection in the mutation step where the individuals are not selected randomly as usual but on the basis of their weighted clustering coefficients. Our enhancement has been incorporated in the classical differential evolution, self-adaptive differential evolution (jDE) and differential evolution with composite trial vector generation strategies and control parameters. Finally, a set of well-known benchmark functions (including 21 functions) has been used to test and evaluate the performance of the proposed enhancement of the differential evolution. The experimental results and statistical analysis indicate that the enhanced algorithms perform better or at least comparable to their original versions and the analysis of the differential evolution dynamics with the aim of the complex network might be an effective tool to improve the differential evolution convergence in the future.

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

From a learning perspective, the mutation scheme in differential evolution (DE) can be regarded as a learning strategy. When mutating, three random individuals are selected and placed in a random order. This strategy, however, probably suffers some drawbacks which can slow down the convergence rate. To improve the efficiency of classic DE, this paper proposes a differential evolution based on improved learning strategy (ILSDE). The proposed learning strategy, inspired by the learning theory of Confucius, places the three individuals in a more reasonable order. Experimenting with 23 test functions, we demonstrate that ILSDE performs better than classic DE.

The Algebraic Differential Evolution (ADE) is a recently proposed combinatorial evolutionary scheme which mimics the behaviour of the classical Differential Evolution (DE) in discrete search spaces which can be represented as finitely generated groups. ADE has been successfully applied to both permutation and binary optimization problems. However, in the previous works, the relationship between ADE and the classical continuous DE has been only intuitively sketched without any theoretical or experimental proof. Here, we fill this gap by providing both theoretical and experimental justifications proving that ADE is a full-fledged generalization of DE which works across different search spaces. First, we formally prove that there exists a concrete implementation of ADE's algebraic operations converging to the classical vector operations of DE, then we propose a real-vector implementation of ADE and we experimentally prove that its behaviour is statistically equivalent to DE. As conclusion, we also pave the way for further applications of the original DE idea to mixed discrete/continuous search spaces.

A new mutation concept is proposed to generalize local selection based Differential Evolution algorithm to work in general multi-modal problems. Three variations of the proposed method are compared with classic Differential Evolution algorithm using a set of five well known test functions and their variants. The general idea of the new mutation operation is to divide the mutation into two parts: the local and global mutation. The global mutation works as a migration operator allowing the algorithm perform global search efficiently, while the local mutation improves the efficiency of local search.The results show that the concept of global mutation is able to generalize the good performance of local selection based Differential Evolution from convex uni-modal functions to general non-convex and multi-modal problems. Among the tested functions, the new method was able to outperform the classic Differential Evolution in all butone. A limited analysis of the effects of control parameters to the performance of the algorithm is also done.

A Differential Evolution Clustering algorithm with weighted validity function is presented in this paper, five validity functions are selected to form the fitness function with weights, and in selection of Differential Evolution, individuals not being selected are put into secondary population. During evolution, individuals in secondary population replace those in main population if their fitness values are less than those in main population. We have carried out experiments on 3 datasets from UCI machine learning repository and compared validity results to those from K-Means and classical Differential Evolution, experimental results show that our approach can improve clustering performance.

Social learning differential evolution

New quantum inspired meta-heuristic techniques for multi-level colour image thresholding

Chapter Ten - Differential evolution

Differential evolution (DE) has been used to solve real-parameter optimization problems with nonlinear and multimodal functions for more than a decade of years. However, it is pointed out that this classical DE harbors restricted efficiency and limited local search ability. Inspired by that gradient-based algorithms have powerful local search ability, we propose a new algorithm, which is diversity-maintained DE based on gradient local search (namely, DMGBDE), by incorporating approximate gradient-based algorithms into the DE search while maintaining the diversity of the population. The primary novelties of the proposed DMGBDE are the following: (1) the gradient-based algorithm is embedded into DE in a different manner and (2) a diversity-maintained mutation is introduced to slow down the learning procedure from the searched best individual. We conduct numerical experiments with a number of benchmark problems to measure the performance of the proposed DMGBDE. Simulation results show that the proposed DMGBDE outperforms classical DE and variant without gradient local search or diversity-based mutation. Moreover, comparison with some other recently reported approaches indicates that our proposed DMGBDE is rather competitive.

Differential Evolution (DE) is a relatively new EA and it has become a major branch of EA. Based on the classical Differential Evolution, we proposed a new Multi-Objective Differential Evolutionary Algorithm in this paper. Compared with NSGA-II and ε-MOEA, the experimental results demonstrate that the new algorithm tends to be more effective in obtaining good convergence and can converge to the true Pareto front with comparable efficiency.Keywordsmulti-objective evolutionary algorithmmulti-objective optimal problemDifferential EvolutionarySpacial Distance

Black box optimization begins with the assumption that if nothing is known about the objective function, then there is no justifiable reason for an optimization algorithm to, e.g. preferentially search in one direction, or to favor one coordinate system orientation over another. This paper investigates whether or not classic differential evolution (DE/rand/1/bin) satisfies these black-box constraints and if not, what it takes to bring the algorithm into conformity with them. The result is an exceptionally simple algorithm, black box differential evolution (BBDE), whose performance is invariant under a coordinate system translation, an orthogonal rotation, a reflection and a permutation of parameters. Performance is also invariant under both the addition of a function bias and an order-preserving transform of the objective function. On the family of ellipsoids, its performance is invariant to both scaling and high-conditioning (eccentricity). Additionally, BBDE is free of both selection and generating drift biases. Furthermore, selection, mutation and recombination are decoupled to become independent operations, as they should be, since each performs a distinctly different function that ought not to be duplicated by another. BBDE also satisfies a few algorithm-specific, symmetry-based constraints. Like the CMA-ES, BBDE's only control parameter is the population size. In short, BBDE appears to be the simplest DE strategy to conform to a set of symmetry-based constraints that are necessary for unbiased, i.e. black box, optimization.

In this paper, a new control parameter adaptation scheme is introduced into the classical differential evolution (DE) algorithm. Then, a method for nonlinear system identification is proposed. The method combines modified differential evolution (MDE) and radial basis function (RBF) neural networks, which can auto-configure the structure of RBF networks and obtain the model parameters. The RBF network structure and parameters could be determined simultaneously based on input-output data without a priori knowledge. Finally, an example of nonlinear function identification is given to illustrate the effectiveness of the proposed approach.

Differential evolution (DE), as a very powerful population-based stochastic optimizer, is one of the most active research topics in the field of evolutionary computation. Self-adaptive differential evolution (SaDE) is a well-known DE variant, which aims to relieve the practical difficulty faced by DE in selecting among many candidates the most effective search strategy and its associated parameters. SaDE operates with multiple candidate strategies and gradually adapts the employed strategy and its accompanying parameter setting via learning the preceding behavior of already applied strategies and their associated parameter settings. Although highly effective, SaDE concentrates more on exploration than exploitation. To enhance SaDE's exploitation capability while maintaining its exploration power, we incorporate local search chains into SaDE following two different paradigms (Lamarckian and Baldwinian) that differ in the ways of utilizing local search results in SaDE. Our experiments are conducted on the CEC-2014 real-parameter single-objective optimization testbed. The statistical comparison results demonstrate that SaDE with Baldwinian local search chains, armed with suitable parameter settings, can significantly outperform original SaDE as well as classic DE at any tested problem dimensionality.